
We used the convention \({w}_{n+1}=0\) . Notice that since the weights \({w}\)  are non-increasing, we have that \({w}_{i}^{\prime }\ge 0\) . Thus, family of admissible OWA weights \({w}\)  yield weights \({w}^{\prime }\)  that are non-negative and sum to 1. This formula offers the interpretation of GGFs as positively weighted averages of points of the generalized Lorenz curves. Every GGF thus corresponds to a scalarization of the multi-objective problem of maximizing every point of the generalized Lorenz curve [1]}, [2]}. We get back to this interpretation in the next subsections.
